Ashley is 4 times as old as Gabriela. Six years ago, Ashley was 7 times as old as Gabriela. How old is Ashley now?
Answer: We can use the given information to write down two equations that describe the ages of Ashley and Gabriela. Let Ashley's current age be $a$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $a = 4g$ Six years ago, Ashley was $a - 6$ years old, and Gabriela was $g - 6$ years old. The information in the second sentence can be expressed in the following equation: $a - 6 = 7(g - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = a / 4$ . Substituting this into our second equation, we get: $a - 6 = 7($ $(a / 4)$ $- 6)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $a - 6 = \dfrac{7}{4} a - 42$ Solving for $a$ , we get: $\dfrac{3}{4} a = 36$ $a = \dfrac{4}{3} \cdot 36 = 48$.